Simferopol, Ukraine (CNN) -- The standoff in Ukraine's Crimea region is a strange one, where soldiers appear to be standing around amid an air of calm. They wear no military insignia, but there's little doubt about who they are.
Russian forces "have complete operational control of the Crimean peninsula," a senior U.S. administration official told CNN, with estimates of 6,000 Russian ground and naval forces in the region. A law is being considered in the Russian parliament that would allow Crimea to be annexed, according to the parliament's website.
Armed men are blocking 10 Ukrainian military and naval bases in Crimea, the newly appointed naval commander of Ukraine, Rear Adm. Serhei Gayduk, told a Ukrainian TV station.
Many ethnic Russians live in Crimea, where support for Russia is strong. Part of Russia's navy -- the Russian Black Sea Fleet -- has a base in Crimea's city of Sevastopol that has been there for 230 years.
In Crimea's capital, Simferopol, soldiers were circling government buildings and patrolling some streets, but their presence did not feel invasive, CNN correspondent Diana Magnay reported Monday.
It appears that there is a "war of information" in the region "between those who watch Russian state TV and those who are getting their news from the West, none of them listening to the calls from Kiev for unity in this country," Magnay reported.
It has been, Magnay says, "a very low-key kind of invasion."
Crimea's First Vice-Premier Rustam Temirgaliyev also described the situation as quiet, Russian state news agency ITAR Tass reported on Monday.
"Despite hysteria in Ukraine's central media, the situation on the peninsula remains absolutely calm. No conflicts have flared up in Crimea over the past 24 hours. Crimea has preserved its inter-ethnic peace," Temirgaliyev said, according to ITAR Tass.
The calmness contrasts with reports that Russia has issued an ultimatum to Ukrainian forces in Crimea to clear out by 5 a.m. Tuesday or face a "military storm," according to a report from Russian state-run news agency Interfax, citing a Ukrainian Defense Ministry source.
Additionally, Ukrainian Defense Ministry spokesman Vladislav Seleznyov told CNN that Russia's Black Sea fleet commander went aboard a blocked Ukrainian warship in Sevastopol harbor on Monday and issued an ultimatum: Swear allegiance to the new Crimean authorities, surrender, or face an attack. The Russian commander, Aleksandr Vitko, did not mention a deadline, Seleznyov said.
But Russia denies plans to storm the Ukrainian military units in Crimea, Interfax said, citing an unidentified spokesman for the Russian Black Sea Fleet. Interfax said the spokesman called these reports "utter rubbish."
"We have gotten used to hearing claims that we are conducting military operations against our Ukrainian colleagues," said the spokesman, adding, "Attempts to set us against each other will fail."
Meanwhile, Seleznyov told CNN that up to 12 trucks full of Russian troops have crossed into the eastern Crimean city of Kerch from Russia.
Additionally, Ukrainian Border Service Assistant Chief Col. Sergei Astakhov described Russian troop movements by ferry from Russia across the Strait of Kerch in a phone conversation.
Astakhov said the first two ferries carrying armed men were navigating toward the ferry dock and border post in Kerch. As the ferries approached the port, 10 heavily armed troops from the Russian Black Sea Fleet attacked the border post from land and used force to overwhelm the Ukrainian border guards, Astakhov said.
The account of the attack contradicts the calm scene that CNN correspondents had observed in Kerch earlier Monday. Close to 100 men in green uniforms, carrying weapons such as AK-47s, lingered outside the main entrance to the ferry port Monday. Soldiers around there were not masked -- they were relaxing, eating and drinking tea, CNN's Ben Wedeman reported.
Half the soldiers were sitting around and waiting, with some standing and others spaced out every 100 meters. They appeared not to be on high alert. One Ukrainian soldier with an insignia remained by the entrance where cars enter the ferry port.
Three six-wheeled military trucks, used for transporting troops, have black license plates indicative of Russian forces based in Crimea, per the agreement between Ukraine and Russia.
An officer who wished to be identified only as Alexander, wearing a hat with the Russian Black Sea Fleet insignia, told CNN he and others from the Sevastopol naval base had been deployed outside the ferry port since Saturday. If they weren't there, he said, "there would be a civil war in Ukraine."
Alexander said the troops are there to protect their Ukrainian brothers from those who seized power locally in Kiev. Ukrainians gave them places to stay and shower, and locals have brought them food, he said.
The troops will stay in Kerch until Crimea decides what it wants to do, Alexander said.
Crimea is the last major stronghold of opposition to the new political leadership in Ukraine. The country's President, Viktor Yanukovych, was ousted February 22 after months of anti-government protests reached a bloody climax. Street clashes between demonstrators and security forces left more than 80 dead.
CNN's Clare Sebastian, Elwyn Lopez, Marie-Louise Gumuchian, Susanna Capelouto, Dana Ford and journalist Emir Shevkiev contributed to this report.